International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue X, October 2017 | ISSN 2321–2705 Strength and Dilatancy of Granular Materials

K.V.S.B. Raju* and Nivya E.C** * Assistant Professor, Department of Civil Engineering, University Visvesvaraya College of Engineering (U.V.C.E), Bangalore University, Bangalore, Karnataka, India ** Formerly Post Graduate Student, University Visvesvaraya College of Engineering (U.V.C.E), Bangalore University, Bangalore, Karnataka, India

Abstract: In the present study an attempt is made to evaluate the Taylor (1948).Followed by Taylor ,Skempton and Bishop strength and dilatancy parameters of glass beads and etched (1950) attempted to separate the strength component (υcv) (rough) glass beads. A series of direct shear tests were performed purely on an account of friction from that (υp -υcv) due to on sample of glass beads and etched glass beads. The size of glass expansion of material; where υp is the angle of internal beads was varied from 1mm-1.7mm,1.7mm-2.36mm and friction corresponding to peak stress ratio. Roscoe et al 2.36mm-4.75mm and mixed together to obtain the required sample. The different relative densities at which tests were .(1958) proved that the critical friction angle (υcv) depends conducted for smooth glass beads are 20%,50% and 80% only on particle shape and material grading. An Ideal method 3 respectively, with corresponding unit weights are 14.1kN/m , for calculating υcv value is plot a graph between υp and 3 3 14.4kN/m and 14.7kN/m respectively and for etched glass beads corresponding rate of dilation. The original stress dilatancy the different unit weights at which tests were conducted are 14.65 model (Rowe 1962) does not capture important behavioral KN/m3,14.93 KN/m3 and 15.2 KN/m3 with corresponding relative features such as density and stress level dependencies. Bishop densities of 30.86%, 54.5% and 76.48% respectively. Most of the (1966) observed that the stress – strain dilatancy behavior of direct shear tests were conducted to shear strain in excess of sand varies remarkable with confining pressures. Bishop 30%. The stress strain response was observed and recorded, and (1972) conducted experiments on steel shots and concluded the shear strength and dilatancy parameters were obtained for each relative density and normal stresses. The normal stress was that an increase in confining pressure leads to a reduction in varied from 50 kPa to 400 kPa. The tests were conducted on the angle of shearing. Bolton (1986) reviewed a large number smooth and etched glass beads; the etched surface of glass beads of triaxial and plane strain test results and proposed a much was obtained by keeping the glass beads in a bath of simpler relationship among υp, υcv and ψp , which he found hydrochloric acid. Also in the present work a correlation operationally equivalent to Rowe (1962)’s stress – dilatancy between peak friction angle, dilatancy angle and critical state relationship; where ψp is the angle of dilatancy which friction angle was obtained for glass beads and etched glass indirectly quantifies the rate of dilation. Bolton (1986) beads. The present data was also compared with those of provided the following simplified expressions: established correlations by Bolton (1986) and Kumar et.al (2007). υp = υcv + 0.8ψp (1)

Keywords: Strength, Dilatancy, Relative density, Peak friction υp = υcv + 5 IR `for plain strain condition (2) angle, Critical state, Correlations, Glass beads υp = υcv + 3 IR for triaxial condition (3)

I. INTRODUCTION The quantity IR is dilatancy index and its magnitude is related n assembly of particles will form a granular material; its to the relative density (DR) and the effective stress (σv) by the A mechanical behavior depends on the size and shape of relationship the particles, their arrangement, particle-to-particle friction, IR =DR(Q-ln(σv))-R (4) associated pore spaces, and the degree of saturation. When deformations take place in granular materials, the external σv expressed in kPa , DR in decimal and Q and R are constants. forces may produce internal fabric changes, which may According to Bolton(1986) observations R=1 and Q=10 was caused by rolling, particles sliding and interlocking, these obtained. Later Salgado et al.(2000) took values as Q=9 and changes will produce a different response of the material R=0.49 from their experiments. behavior. Considerations of such material response are extremely significant in the design of soil structures such as Kumar et al. (2007) examined further the correlations between retaining walls, foundations systems, and dams, because the υp, υcv, ψp and IR by conducting series of direct shear tests on analyses of these systems are based on the strength and Bangalore sand. Kumar et al. (2007) provided the following deformation behavior of the material bottom or near to them. empirical relations According to Reynolds observations (1885) the dense sand υp = υcv + 0.932ψp (5) exhibit expansion in volume during shear and loose sand contract during shear deformation. The role of volume υp = υcv + 3.5 IR `for plain strain condition (6) changes during shear especially dilatancy was recognized by

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International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue X, October 2017 | ISSN 2321–2705

IR =DR(10-ln(σv))-1 with σv is expressed in kPa and DR expressed in decimals. The objective of the present study is to examine further these correlations on glass beads. For this purpose series of direct shear tests were conducted on smooth and etched glass beads and also to find the effect of surface roughness on strength and dilatancy of etched glass beads. Tests were conducted by varying normal stress from 50 kPa to 400 kPa with three different relative densities of sample. All the tests were conducted for both smooth and etched glass beads sample. Each tests was continued till the achievement of the critical state of the sample. The values of υp and ψp were determined for each test for different combinations of relative density and normal stress values. All the test results were compared with recommendations of Bolton (1986) and Kumar et al.(2007) so as to suggest correlations which provides better estimation Fig. 2Grain size Distribution Curve of rough glass beads with regard to the present experimental data on glass beads. III. EXPERIMENTAL PROCEDURE II. MATERIALS A series of direct shear tests were conducted on smooth glass Materials used in this experiment were smooth glass beads beads at three different relative densities namely 20%, 50% and etched (Rough) glass beads. Three different sized glass and 80% the corresponding unit weights are 14.1 KN/m3, 14.4 beads varying from 4.75 mm -2.36 mm, 2.36 mm-1.7 mm and KN/m3 and 14.7 KN/m3 respectively and on rough glass beads 1.7 mm-1 mm were mixed together to form the desired sample at different unit weights namely 14.65 KN/m3,14.93 KN/m3 of glass beads. The particle size distribution of the materials is and 15.2 KN/m3 with corresponding relative densities shown in Figure 1. The specific gravity of smooth glass beads 30.86%,54.5% and 76.48% respectively. The size of shear box obtained was 2.6 and that for rough glass beads it was 2.58. was 60 mm X 60mm and the sample height was kept at 25 The maximum and minimum unit weights of smooth glass mm for all the tests. All the tested samples were sheared at a beads obtained was 14.9 KN/m3 and 13.9 KN/m3 respectively constant shear strain rate of 0.625 mm/minute between the and for rough glass beads maximum and minimum unit two halves of shear box. The normal stresses for all tested weights obtained was 15.5 KN/m3 and 14.3 KN/m3 samples was varied from 50 kPa to 400 kPa. The samples of a respectively. The different parameters obtained from grain given density were prepared by either raining the materials size distribution curve of the glass beads are D10= 1.4 mm, from a constant height of fall (for loose and medium dense D30=2 mm, D50=2.6 mm, D60=2.9 mm, Cu=2.07 and Cc=0.99; condition) or with the tamping technique using a fixed number D10, D30, D50 and D60 are respective percentage of finer, and of blows (for dense condition). All the tests were continued up Cu and Cc are the uniformity coefficient and the coefficient of to u/H =40%; where u is the horizontal displacement at any curvature of the glass beads respectively. As per IS 1498-1970 time and H is the initial height of the sample. sample is said to be poorly graded. Etched glass beads also giving same particle size distribution curve, as that of smooth glass beads; that means etching process does not affect the uniformity coefficient and the coefficient of curvature values.

(a)

Fig. 1Grain size Distribution Curve of smooth glass beads

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International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue X, October 2017 | ISSN 2321–2705

then followed by a decrease in the shear stress which ultimately leads to the critical state of the material at very high values of horizontal displacement; in such cases the material initially shows a decrease in volume followed by an increase in volume it is observed both in the case of smooth glass beads and rough glass beads. At low values of σv, the rate of dilation becomes maximum corresponding to υp and subsequently the value of dilatancy angle again decreases and finally becomes equal to zero in the critical state. On the contrary at very high values of σv, the behaviour of the material remains similar to that of loose sand where the shear stress increases continuously to yield the critical state at very high values of horizontal displacement. In such cases the

material experiences a continuous decrease in (b) volume until reaching the critical state. Fig. 3. SEM photographs of (a) rough glass bead and (b) smooth glass bead Figure 3 shows SEM photographs of rough and smooth glass bead. It is noticed from the Fig.3, the change in surface texture of rough glass beads, then when compared to smooth glass beads. IV. TEST RESULTS For all the tests, the variation of the horizontal (shear) force (Ph) and the corresponding change (v) in the vertical height of the sample with increase in the horizontal displacement (u) was continuously monitored at regular time interval; volumetric strain simply becomes equal to v/H. The corresponding test results are shown in Figures 3 - 8 in terms of (i) the variation of Ph/Pv with u/H, and (ii) the variation of v/H with u/H; where Pv is the magnitude of the vertical force. From these plots the values of friction angles (υ) and dilatancy angles (ψ) were determined using the following expressions: (a)

Φp and ψp are the peak values of Φ and ψ respectively. Variations of Φp and ψp with variations of normal stress (σv) is illustrated in fig .9 for smooth and rough glass beads.  The peak values of υ and ψ invariably occur almost at the same value of the horizontal displacement in the case of rough glass beads ,but in the case of smooth glass beads peak values are not occurring at the same horizontal displacement. An increase in the relative density of the material causes a marginal (b) decrease in the value of u/H associated with υp.  For a given relative density of the material, the Fig. 3 For γ = 14.1 kN/m3 smooth glass beads, the observed variation of (a) Ph/Pv with u/H, and (b) v/H with u/H behaviour of the material at low stress level always remains typically that of a dense sand which indicates a well defined peak corresponding to υp and

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International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue X, October 2017 | ISSN 2321–2705

(a) (b) Fig.5 For γ = 14.4 kN/m3 smooth glass beads, the observed variation of (a) Ph/Pv with u/H, and (b) v/H with u/H

Correlation between Φp and Ψp

For varying values of σv and relative density (Dr) of the material, obtained values of υp were plotted against corresponding values of ψp. All the data points are indicated in Fig.11 (a) and (b) for smooth and rough glass beads respectively. The following correlations are obtained for the present data :

υp = υcv +1.3434 ψp for smooth glass beads (9) (b) υp = υcv + 0.8577ψp Fig.4 For γ = 14.65 kN/m3 rough glass beads, the observed variation of (a) Ph/Pv with u/H, and (b) v/H with u/H for rough glass beads (10) It is very well known from the figure 11 that the value  The values of υp as well as ψp decrease with increase of υ for the chosen smooth glass bead sample is found to be in the value of σv. As compared to loose sand, the cv equal to 21.471o and for rough glass bead sample found to be effect of σv on the changes in the values of υp and ψp was seen to be more significant in the case of dense 36.72 (that is τ/σv = 0.8). It can also be noticed from Figures sand. 3-8 that the value of τ/σv at very large value of u/H (30-40%) remains very close to 0.80 indicating the achievement of the  For a given value of σv, an increase in the relative density of the material causes an increase in the same critical state in all the tests for rough glass beads. values of both υp and ψp.

(a) (a)

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International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue X, October 2017 | ISSN 2321–2705

(b) (a) Fig.6 For γ = 14.93 kN/m3 rough glass beads, the observed variation of (a) Ph/Pv with u/H, and (b) v/H with u/H A comparison of Equations (1),(5),(9) and (10) indicates that the variation of Bolton (1986) recommendation was more for smooth glass beads but it compares very well with respect to rough glass beads.

(b) Fig.8 For γ = 15.2kN/m3 rough glass beads, the observed variation of (a) Ph/Pv with u/H, and (b) v/H with u/H

Correlation between φp and σv

As seen earlier from Figure 8 that the value of υp reduces with (a) increase in the value of σv. According to Bolton’s observations obtained equation (2) and also according to Kumar et al equation (6) obtained, where IR (dilatancy index) is defined by Equation (4) with Q = 10 and R = 1. From the regression analysis following equation is suitable for present data.

υp = υcv + 4.7 IR for smooth glass beads (11)

υp = υcv + 3.2 IR for rough glass beads (12)

where IR =DR(10-ln(σv))-1 with σv expressed in kPa and DR in decimal.

(b) Fig.7 For γ = 14.7 kN/m3 smooth glass beads, the observed variation of (a) Ph/Pv with u/H, and (b) v/H with u/H

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International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue X, October 2017 | ISSN 2321–2705

(b)

Fig. 10 The correlation between υ and shear strain from all the test results (a) p (a)for smooth glass beads (b) for rough glass beads

Experimentally measured values of υp - υcv is plotted against estimated values of the observations of Bolton (1986), Kumar et al (2007) and present correlation was shown in Fig.12, and it was found that the present data on smooth and rough glass beads reasonably compares well with that of Bolton(1986) and Kumar et.al., (2007)

(b)

Fig. 9 The variation of υp and ψp with σv (a) smooth glass beads and (b) rough glasss beads

(a)

(a) (b)

Fig. 11 The correlation between υp and ψp from all the test results (a) for smooth glass beads (b) for rough glass beads

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International Journal of Research and Scientific Innovation (IJRSI) | Volume IV, Issue X, October 2017 | ISSN 2321–2705

correlating  p with and has also been provided for smooth and rough glass beads on the basis of which the value of can also be predicted. The suggested expressions are found to match well with the test results. Based on the test results, it can be concluded that decrease in σv leads to an increase in the values of and which necessitates the need of employing secant values of rather than tangent , with some small value of an apparent cohesion. It was also concluded from the test results the values of and not only depends on stress level and density but also on the surface texture of glass beads.

(a) REFERENCES [1]. Bishop, A. W. (1966): “The Strength of Soils as Engineering Materials”, Geotechnique, 16(2), pp. 91-128. [2]. Bishop, A. W. (1972): “Shear Strength Parameters for Undisturbed and Remoulded Soil Specimens”, In Stress-Strain Behaviour of Soils, R.H.G. Parry, (Ed.), London: Foulis, pp. 3-58. [3]. Bolton, M. D. (1986): “The Strength and Dilatancy of Sands”, Geotechnique, 36(1), pp. 65-78. [4]. Casagrande, A. (1936): “Characteristics of Cohesionless Soils affecting the Stability of Slopes and Earth Fills”, Journal of Boston Society of Civil Engineers, 23(1), pp. 13-32. [5]. IS-1498-1970, Reaffirmed (2002): “Classification and Identification of Soils for Engineering Purposes”, Bureau of Indian Standards, New Delhi. [6]. Kumar, J. Raju, K. V. S. B., and Kumar,A(2007):Relationship between rate of dilation, peak and critical state friction angles, Indian Geotechnical Journal, Vol 37(1),No.1, 53 – 63 [7]. Raju K.V.S.B and Mohamed Shoaib Khan (2014)“The effect of grading on strength and dilatancy parameters of sands” Proc Indian Geotechnical Conference, IGC – Kakinada, 168-176 [8]. Reynolds, O. (1885): “The Dilating of Media Composed of Rigid (b) Particles in Contact”, Philosophical Magazine, December issue. [9]. Roscoe, K. H. (1953): “An Apparatus for the Application of Fig 12 The prediction of (υp-υcv) using different formulae against measured Simple Shear to Soil Samples,” Proc. of the 3rd Int. Conf. Soil values of (υp-υcv) for all the tests (a) for smooth glass beads and (b) for rough Mech. and Found. Engg., Zurich,1, pp. 186 - 191. glass beads [10]. Roscoe, K. H., Schofield, A. N. and Wroth, D. P. (1958): “On the Yielding of Soils”, Geotechnique, 9, pp. 22-53. V. CONCLUSIONS [11]. Rowe, P. W. (1962): “The Stress-Dilatancy Relation for Static Equilibrium of an Assembly of Particles in Contact”, Proc. Royal Based on a number of direct shear tests on smooth and rough Soc., London, 269 A, pp. 500-527. glass beads, at different density states and stress level, an [12]. Salgado, R., Bandini, P. and Karim, A. (2000): “Shear Strength and Stiffness of Silty Sand”, Journal of Geotechnical and empirical relationship correlating  p , cv and IR similar to Geoenvironmental Engineering, ASCE, 126 (5), pp. 451-462. [13]. Skempton, A. W. and Bishop, A. W. (1950): “Measurement of that recommended by Bolton (1986), Kumar et al. (2007), has Shear Strength of Soils”, Discussion by A.W. Bishop, been suggested. Using this relationship from the knowledge of Geotechnique, 4 (2), pp. 70. [14]. Taylor, D. W. (1948): Fundamentals of Soil Mechanics, John relative density (Dr) and critical state friction angle ( ), the Wiley and Sons, New York. value of peak friction angle can be determined for any required effective stress level (σv). Further, an expression

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